An Access Point Name (APN) is a gateway between a GSM, GPRS, 3G or 4G mobile network and another computer network, frequently the public Internet. A mobile device making a data connection must be configured with an APN to present to the carrier.
The APN is used to find the right IP address that the device should be identified with on the network, determine if a private network is needed, choose the correct security settings that should be used... etc. If you sign up with a Mobile Virtual Network Operator (MVNO), which leases broadcast spectrum from the big carriers, you might need to configure your phone’s APN settings.
In the US, the APN name is often "wholesale".
APN type: Generic, SUPL, MMS, and WAP are the four different APN types. Generic should be used if there are problems when you're setting up these options.
MMSC (see Multimedia Messaging Service): is only necessary if you're using MMS. It's a requirement on most MVNOs (see Mobile Virtual Network Operators) that use MMS.
Proxy: Some mobile carriers will use this setting to set up a proxy between the network and the Internet, much the same as a proxy on a computer.